The Tulczyjew triple in mechanics on a Lie group
Marcin Zaj\k{a}c, Katarzyna Grabowska
TL;DR
This paper develops a geometric framework called the Tulczyjew triple for mechanical systems on Lie groups, including reduction techniques for symmetric systems, and applies it to analyze free rigid-body dynamics.
Contribution
It introduces a Tulczyjew triple tailored for Lie group configuration spaces and extends it with reduction methods for symmetric systems, applied specifically to rigid-body motion.
Findings
Constructed the Tulczyjew triple for Lie group systems
Developed reduction procedures for symmetric systems
Applied the framework to free rigid-body dynamics
Abstract
Tulczyjew triple for physical systems with configuration manifold equipped with Lie group structure is constructed and discussed. The case of systems invariant with respect to group acton is considered together with appropriate reduction of the Tulczyjew triple. The theory is applied to free rigid-body dynamics.
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Taxonomy
TopicsDynamics and Control of Mechanical Systems · Geotechnical and Geomechanical Engineering · Geophysics and Sensor Technology